Methods and Apparatus for Stimulation of Biological Tissue

ABSTRACT

In illustrative implementations of this invention, interferential stimulation is precisely directed to arbitrary regions in a brain. The target region is not limited to the area immediately beneath the electrodes, but may be any superficial, mid-depth or deep brain structure. Targeting is achieved by positioning the region of maximum envelope amplitude so that it is located at the targeted tissue. Leakage between current channels is greatly reduced by making at least one of the current channels anti-phasic: that is, the electrode pair of at least one of the current channels has a phase difference between the two electrodes that is substantially equal to 180 degrees. Pairs of stimulating electrodes are positioned side-by-side, rather than in a conventional crisscross pattern, and thus produce only one region of maximum envelope amplitude. Typically, current sources are used to drive the interferential currents.

RELATED APPLICATIONS

This application is a non-provisional of, and claims the priority of,U.S. Provisional Patent Application No. 62/061,349, filed Oct. 8, 2014,the entire disclosure of which is herein incorporated by reference.

FIELD OF TECHNOLOGY

The present invention relates generally to stimulation of biologicaltissue, including interferential stimulation of a brain.

SUMMARY

In illustrative implementations of this invention, interferentialstimulation is precisely directed to arbitrary regions in a brain. Theregion targeted is not limited to the area immediately beneath theelectrodes, but may be any superficial, mid-depth or deep brainstructure. For example, in some use scenarios of this invention,interferential stimulation is precisely targeted at a deep brainstructure, such as the thalamus, hypothalamus, amygdala, or hippocampus.In other use scenarios, interferential stimulation is precisely targetedon a superficial or mid-depth region of the cortex. In yet other usescenarios, interferential stimulation is precisely targeted on both asuperficial brain structure and deep brain structure simultaneously.

Conventional interferential current (IFC) devices and methods are notable to achieve this targeting, because they suffer from at least fourflaws:

First, targeting by conventional IFC is based on a misconception: It iserroneously believed that maximum cell response occurs in regions wherethe modulation index of the amplitude-modulated (AM) waveform approaches100%. In other words, the misconception is that the greater theinterference between the two original waveforms that create the AMwaveform, the better the interferential therapy works. Thus, based onthis misconception, conventional IFC tries to position the region ofmaximum interference (i.e., where the amplitudes of the two originalwaveforms that form the AM wave are closest to being equal) at thetissue structure that is the target of the attempted stimulation.

This belief is incorrect. In fact, the maximum cell response tointerferential stimulation occurs in the region where the envelopeamplitude (as defined herein) of the AM waveform is greatest. The regionwhere the envelope amplitude is greatest does not necessarily coincidewith the region of maximum interference, and is often quite different.Examples of envelope amplitude E_(AM) are shown in FIGS. 1A, 1C and 1D.

Second, conventional IFC suffers from significant current leakagebetween the two current channels that create the interferential effect.An IFC device typically uses two pairs of stimulating electrodes. Eachelectrode pair is a current channel that creates an electric field. Theinterference of the two electric fields produces the AM waveform thatstimulates cells in interferential therapy. Unfortunately, inconventional IFC, substantial current leakage occurs between the twochannels—for example, in some cases, 20% or more of the current acrossone electrode pair is due to the electric waveform created by the otherelectrode pair. This crosstalk between current channels may cause thespatial position of interference regions to shift in an undesirable oruncontrolled way. For example, because current from one electrode pairis flowing into the other electrode pair, cell stimulation due to an AMwaveform may occur very near the electrodes, even if stimulation isdesired to occur at a position remote from the electrodes. This leakagebetween currents occurs because both pairs of electrodes areelectrically connected to the same conductive load—the tissue of thesubject being stimulated. In some existing IFCs, transformers have beenused to isolate currents. However, transformers tend to be bulky.

Third, in conventional IFC, electrode placement is limited. Inconventional IFC, the four stimulating electrodes are positioned in acrisscross pattern, in which each electrode is located at a corner of arectangle (typically, a square). Thus, the line segment that joins theelectrodes of one electrode pair is one diagonal of the rectangle, andthe line segment that joins the electrodes of the other electrode pairis the other diagonal of the rectangle. These two diagonals cross eachother, forming an X (crisscross) pattern. The electrodes are positionedso that the target tissue region is located at, or beneath, the centerof the rectangle where the two crisscrossing diagonals intersect. Thiscrisscross pattern is consistent with (and perhaps was originallymotivated by) the misconception described above: in this configuration,the region of maximum interference typically would occur (absent thespatial inaccuracies caused by current leakage) at the center of therectangle where the two diagonals intersect. Unfortunately, thisconventional electrode placement is not suited for targeting some tissueregions, such as deep brain structures remote from the stimulatingelectrodes. For example, it is typically impossible to positionelectrodes on the skin in a rectangular pattern such that thehypothalamus (a deep brain structure) is located at the center of therectangle.

Fourth, in many conventional IFC devices, voltage sources are used todrive the current channels. Unfortunately, the amount of currentdelivered by a voltage source depends on the impedance of the electricalload. This problem is exacerbated where the conductive load is a brain,because impedance varies widely in different brain structures, making itdifficult to deliver a precisely regulated current amount with voltagesources. This in turn makes it difficult to precisely control thespatial position of the interferential stimulus in the brain.

In illustrative embodiments of this invention, a novel interferentialstimulation technology overcomes these four hurdles as follows:

First, in illustrative embodiments, targeting is based on achieving adesired envelope amplitude at targeted tissue locations. For example, insome cases, the region of maximum envelope amplitude is positioned atthe specific brain structure being targeted. Or, for example, a largerregion may be targeted, and the interference tuned such that theenvelope amplitude is simultaneously above a certain threshold in allparts of the targeted region.

Second, in illustrative embodiments, currents are isolated by making atleast one of the current channels anti-phasic: that is, the electrodepair of at least one of the current channels has a phase differencebetween the two electrodes that is substantially equal to 180 degrees.This dramatically reduces current leakage between the two currentchannels. For example, in a prototype of this invention, current leakagebetween the two current channels has been reduced such that only 4% ofthe current across one electrode pair is due to the electric fieldcreated by the other current channel. Thus in illustrative embodiments,the anti-phasic current channel(s) greatly ameliorate current leakage,which in turn allows the interferential device to more preciselyposition the region in which the envelope amplitude is at a desiredmagnitude.

Third, in illustrative embodiments, stimulating electrodes arepositioned in a wide variety of spatial configurations, includingpositions in which the electrodes are not in rectangular (or square)configuration. For example, in some embodiments of this invention: (a)the stimulating electrodes are positioned in a semicircle, or circle, orline; or (b) the stimulating electrodes are positioned such that thedistance between electrodes of one electrode pair (current channel) isdifferent than the distance between electrodes of the other electrodepair (current channel) or is different than the distance between the twoelectrode pairs; or (c) the stimulating electrodes are positionedside-by-side, rather than in a crisscross pattern. Thus, in illustrativeembodiments, the positioning of electrodes is adaptable to the structurebeing stimulated, and may be selected so as to control the spatialposition of regions in which the envelope amplitude is above a giventhreshold.

Fourth, in illustrative embodiments, current sources are used to drivethe interferential currents, rather than voltage sources. An advantageof a current source is that the current delivered does not, within thesource's compliance voltage range, depend on the impedance of the load.Thus, the amount of current can be precisely controlled, despite theanistropic impedance of the brain. This, in turn, facilitates preciseinterferential targeting, because the spatial position of a region witha given envelope amplitude depends in part on the magnitude of thecurrents in the two interferential current channels.

This invention is not limited to stimulation of the brain, but haspractical advantages in a wide variety of use cases. Among other things,in illustrative embodiments of this invention, interferentialstimulation may be precisely targeted at any deep or superficial regionof the body. For example, in some use scenarios of this invention,interferential stimulation is targeted at particular regions of theheart, or at the pineal gland deep inside the cranium, or at the spinalcord or other nerves, or at the digestive tract, or at reproductivetissue, or at a muscle.

This invention is not limited to interferential stimulation. Among otherthings, current isolation using an anti-phasic current channel may beemployed to simultaneously deliver stimulation at different frequenciesto different tissue regions, in such a manner that the tissue respondsto the original waveforms, and not to the AM waveform created byinterference.

The description of the present invention in the Summary and Abstractsections hereof is just a summary. It is intended only to give a generalintroduction to some illustrative implementations of this invention. Itdoes not describe all of the details and variations of this invention.Likewise, the descriptions of this invention in the Field of Technologysection and Field Of Endeavor section are not limiting; instead theyeach identify, in a general, non-exclusive manner, a technology to whichexemplary implementations of this invention generally relate. Likewise,the Title of this document does not limit the invention in any way;instead the Title is merely a general, non-exclusive way of referring tothis invention. This invention may be implemented in many other ways.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a conceptual diagram that illustrates envelope amplitude.

FIG. 1B illustrates an example in which the region of maximuminterference does not overlap with the region of maximum envelopeamplitude.

FIGS. 1C and 1D show the envelope amplitude at two regions of FIG. 1B.

FIGS. 1E, 1F, 1G, 1H, 1I, 1J, 1K, and IL show examples of electrodeconfigurations.

FIG. 1M shows examples of geometric shapes along which electrodes may bepositioned, in illustrative implementations of this invention.

In some cases, the stimulating electrodes are arranged in a

FIGS. 2A, 2B, 2C, 2D, 2E, 2F, 2G and 2H show neural responses to atime-varying electric field.

FIG. 3 shows a conventional (prior art) apparatus for applying multiplecurrents to a common conductive load.

FIGS. 4A, 4B and 4C each show examples of an anti-phasic current drivefor applying isolated currents to a common conductive load.

FIG. 4D shows an example of a current drive that includes an isolationtransformer, and that is configured to apply isolated currents to acommon conductive load.

FIGS. 5A, 5B, 5C, 5D, 5E, 5F, 5G, 5H, 5I, 6A, 6B, 6C, 6D, 6E, 6F, 6G,6H, and 6I show measured values of electrical fields in a 2D phantom.

FIG. 7 shows an example of side-by-side positioning of electrode pairs.

FIG. 8 shows a conventional (prior art) zero-mean envelope AM electricfield.

FIG. 9 shows a non-zero-mean envelope AM waveform formed bysuperposition of two temporally asymmetric waveforms.

FIG. 10 shows a non-zero-mean envelope AM waveform formed bysuperposition of two waveforms that are amplitude offset from eachother.

FIG. 11 shows hardware components of an anti-phasic current drive.

FIG. 12 shows hardware components of a current drive that includes anisolation transformer.

FIG. 13 shows hardware components of a voltage drive that isanti-phasic.

FIG. 14 shows hardware components of a voltage drive that includes atransformer.

FIGS. 15A, 15B, 15C, 15D, 15E and 15F show examples of electrodespositioned on neuromodulation targets.

FIGS. 1-2G, 4A-4D, 5B, 5F, 5G, 5K, 6C, 6H, 6I, 6L, 7, and 9-15E showillustrative implementations of this invention, or provide informationthat relates to those implementations. However, this invention may beimplemented in many other ways.

DETAILED DESCRIPTION Targeting Based on Envelope Amplitude

FIG. 1A is a conceptual diagram that illustrates envelope amplitude. InFIG. 1A, two current channels produce two original waveforms: channel 1produces original waveform 111 and channel 2 produces original waveform112. The amplitude of the first waveform 111 is E_(ch1); and theamplitude of the second waveform 112 is E_(ch2). The AM index is theratio of these two amplitudes: AM index=E_(ch1)/E_(ch2). Interference ofthe two original waveforms 111, 112 produces an amplitude-modulated (AM)waveform 114. The AM waveform has an envelope 115. The top of theenvelope is a signal. The peak amplitude of that signal is the envelopeamplitude E_(AM).

In illustrative embodiments of this invention, targeting is based on theenvelope amplitude instead of the AM index. Specifically, inillustrative embodiments, targeting is based on controlling the spatialposition of a region where the envelope amplitude is above a thresholdor is at a maximum. This is different than conventional IFC, in whichtargeting attempts to control the spatial position of a region where theAM index is above a threshold or is at a maximum.

This distinction is important, because the region of maximum envelopeamplitude does not necessarily coincide with the region of maximuminterference, and is often quite different.

FIG. 1B illustrates an example in which the region of maximuminterference does not overlap with the region of maximum envelopeamplitude. In FIG. 1B, a first current channel runs through a first pairof electrodes 121, 122. The second current channel runs through a secondpair of electrodes 123, 124. The two pairs of electrodes areelectrically connected to a common conductive load 125 (such as abrain). Arrows 126 and 127 represent the current from the first andsecond current channels, respectively, flowing in the conductive load125. The arrows are merely symbolic—among other things, each currentactually alternates in direction and flows through all regions of theconductive load.

In FIG. 1B, maximum envelope amplitude occurs in regions 128 and 129,but the region of maximum interference (where the electric field has thehighest AM index) occurs at region 130.

FIGS. 1C and 1D show the envelope amplitude at two regions of FIG. 1B.Specifically, FIG. 1C shows the AM waveform 141 at region 128, and FIG.1D shows the AM waveform 142 at region 130. The envelope amplitude islabeled E_(AM).

The interference at region 130 is complete (modulation index is 100%) asshown in FIG. 1D. The interference at region 128 is less than complete(modulation index is less than 100%) as shown in FIG. 1C.

However, E_(AM) (that is, the envelope amplitude) is greater at region128 as shown in FIG. 1D, and is less at region 130 as shown in FigureAC.

Conventional IFC therapy would attempt to position region 130 at thetarget tissue, because region 130 has the maximum interference(modulation index=100%).

In contrast, an illustrative implementation of this invention wouldposition region 128 or region 129 at the target tissue, because envelopeamplitude is greatest in regions 128 and 129.

The size, shape and position of a region where the envelope amplitudeexceeds a given threshold depends on the relative amplitudes of the twocurrent channels and on the placement of the electrodes for the twochannels. In illustrative embodiments of this invention, these factorsare adjusted to precisely position this region at the targeted tissue.For example, in some use scenarios of this invention involvinginterferential stimulation, transcranial electrodes create electricfields in a brain such that: (i) an interferential zone is created closeto one or more of the electrodes at a superficial depth in the brain(e.g. in the cortex); (ii) an interferential zone is created at a deeperdepth of the brain but laterally close to the electrodes; or (iii) aninterferential zone is created at any brain depth in a region that it isremote from the electrodes. In some cases, relative amplitude of the twooriginal waveforms is used to control the size and location of aninterferential zone in a brain.

In some embodiments of this invention, the first electrode pair andsecond electrode pair are positioned such that, at a given time, thelargest magnitude of the envelope amplitude occurs in only one region ofthe brain. This region is path-connected and consists only of thosepoints at which the largest magnitude of the envelope amplitude occurs.This region of highest envelope amplitude may be precisely targeted. Forexample, in some use cases of this invention, this region of highestenvelope amplitude is positioned such that the region spatiallycoincides with (i) cortical tissue of a brain, (ii) subcortical tissueof a brain; (iii) heart tissue, or (iv) tissue in a nerve. Moregenerally, in illustrative embodiments of this invention, this region ofhighest envelope amplitude is precisely positioned on target tissueanywhere in the body.

In some embodiments of this invention: (a) the amplitude modulatedwaveform has an envelope amplitude; (b) the greatest magnitude of theenvelope amplitude occurs in a spatial position in the brain; (c) avolume exists, which volume consists of only those points at which themagnitude of the envelope amplitude is equal to at least 50% of thegreatest magnitude; and (d) this volume coincides with both cortical andsubcortical tissue of the brain.

Electrode Placement

In conventional IFC, the four stimulating electrodes are positioned in acrisscross pattern, in which each electrode is located at a corner of arectangle (typically, a square). Thus, the line segment that joins theelectrodes of one electrode pair is one diagonal of the rectangle, andthe line segment that joins the electrodes of the other electrode pairis the other diagonal of the rectangle. These two diagonals cross eachother, forming an X (crisscross) pattern. The electrodes are positionedso that the target tissue region is located at, or beneath, the centerof the rectangle where the two crisscrossing diagonals intersect.

The electrode placement in FIG. 1B is an example of this conventionalconfiguration. In FIG. 1B, the four electrodes 121, 122, 123, 124 arelocated at the four corners of a geometric rectangle 140. Arrows 126 and127 coincide with the two diagonal lines that join opposite corners ofthe rectangle. In conventional IFC, the electrodes are positioned sothat the target tissue is at, or beneath, the intersection of these twodiagonals—that is, at or beneath position 130.

In contrast, electrode placement is more flexible, in illustrativeembodiments of this invention.

A rectangular configuration may be used with this invention (e.g., totarget regions 128 or 129 in the example shown in FIG. 1B or to targetregions 181, 182, 183, 184 in FIG. 1E). However, a rectangularconfiguration of stimulating electrodes is usually not desirable, forthe reason discussed in the next paragraph, and so other electrodeplacements are typically used in illustrative embodiments of thisinvention.

FIGS. 1B and 1E illustrate a drawback of a conventional, crisscrossconfiguration, in which two geometric line segments (one of which isbetween the electrodes in the first current channel and the other ofwhich is between the electrodes in the second current channel) intersector cross over each other. This drawback is that the crisscrossedelectrodes produce multiple, separate regions (such as regions 128 and129 in FIG. 1B, and regions 180, 182, 183, 184 in FIG. 1E) where themaximum envelope amplitude occurs. In typical use scenarios in which itis desired to provide interferential stimulation to only a singletargeted location, the extra regions of maximum envelope amplitude arenot desirable, since they stimulate at least one additional tissueregion that is not an intended target. (Of course, if one is under theconventional misconception that the region of maximuminterference—rather than the region of maximum envelope amplitude—shouldbe positioned at the targeted tissue, this drawback is not apparent. Theregion of maximum interference typically occurs at the center of theconventional rectangular configuration where the crisscross intersects).

FIGS. 1F to IL show examples of electrode configurations, inillustrative implementations of this invention. In the examples shown inFIGS. 1E to IL, only one region 180 of maximum envelope amplitudeoccurs. This is advantageous, because in typical use scenarios, only onetissue is being targeted at a time, and thus it is advantageous toproduce only one region of maximum envelope amplitude at time. Theresponse of neurons (or other excitable cells) to the interferentialstimulation is greatest where the envelope amplitude is greatest (atleast, for amplitudes within the safe operating ranges of aninterferential device treating a human).

A reason that only one region 180 of maximum envelope amplitude isproduced in FIGS. 1F to IL is that the pairs of electrodes arepositioned side-by-side, rather than in a crisscross configuration. Asused herein, a first pair of electrodes and a second pair of electrodesare positioned “side-by-side” if, for a first line segment that joinsthe electrodes of the first pair and a second line segment that joinsthe electrodes of the second pair, a geometric plane exists such that(i) the first line segment is positioned entirely on one side of theplane; (ii) the second line segment is positioned entirely on the otherside of the plane; and (ii) neither the first line segment nor thesecond line segment intersect the plane. An example of a side-by-sideconfiguration, showing such a geometric plane, is illustrated in FIG. 7.

In the examples FIGS. 1F to IL, the electrode placement isunconventional, because the electrode pairs are positioned side-by-side,rather than in a crisscross pattern.

In FIGS. 1F to IL, the gray region 180 is the region of greatestenvelope amplitude. Electrodes 121 and 122 are the electrode pair forthe first current channel. Electrodes 123 and 124 are the electrode pairfor second current channel. Distance a is the distance between the twoelectrodes 123, 124 of the second electrode pair. Distance b is thedistance between the two electrodes 121, 122 of the first electrodepair. Distance c is the distance between electrode 122 (in the firstelectrode pair) and electrode 124 (in the second electrode pair.Distance d is the distance between electrode 121 (in the first electrodepair) and electrode 123 (in the second electrode pair). Distance e isthe distance between electrode 121 (in the first electrode pair) andelectrode 124 (in the second electrode pair. Distance f is the distancebetween electrode 122 (in the first electrode pair) and electrode 123(in the second electrode pair).

FIG. 1E shows an example of a conventional electrode configuration,which may be used in this invention. In FIG. 1E, the electrodes are atthe four corners of a square, and the electrode pairs are arranged in acrisscross pattern. In FIG. 1E, four separate regions 180, 182, 183, 184of maximum envelope amplitude occur. This is usually disadvantageous,for the reasons discussed above.

FIGS. 1F to IL show non-conventional electrode placements forinterferential stimulation, which may be used in this invention.

In FIG. 1F, the electrodes are in a rectangular pattern, such thata=b<c=d.

In FIGS. 1G to IL, the electrodes are not positioned at the corners of ageometric rectangle. In FIG. 1G, a=b<c<d. In FIG. 1H, c<d<a=b. In FIG.1I, c<e=f<d. In FIG. 1J, c<a=b<d.

In FIG. 1K, the four electrodes 123, 124, 121, 122 are arranged in astraight line.

In FIG. 1L, the four electrodes 121, 122, 123, 124 are positioned at thecorners (vertices) of a parallelogram that is not a rectangle.

FIG. 1M shows examples of geometric shapes along which electrodes may bepositioned, in illustrative implementations of this invention.

In some cases, the stimulating electrodes are arranged in a circle,semicircle, straight line or almost straight line. In some cases, all ofthe stimulating electrodes are positioned in a single plane, such astransverse plane 131, plane 132 (perpendicular to the longitudinal axisof a nerve), coronal plane 133, or sagittal plane 134. In some cases,the stimulating electrodes are placed in a straight line, as shown inFIG. 1K, or almost in a straight line. For example, in some case, theelectrodes may be positioned on a slightly curved line segment 135 thattouches, and conforms to the curvature of, the exterior of a head. Insome cases, electrodes are positioned in a straight line along a probethat is inserted to a brain, such as electrodes 1525, 1526, 1527, 1528which are disposed in a straight line near the tip of probe 1521, asshown in FIGS. 15C and 15D.

Modulation of Excitable Cells

In some implementations of this invention, an apparatus drives multipleelectric currents through tissue comprising excitable cells in such amanner as to modulate activity of the tissue. In many cases: (a) themodulation occurs in spatial regions that are remote from thestimulating electrodes; and (b) the modulation is less pronounced orabsent in regions closer to the stimulating electrodes. For example, theexcitable cells may comprise neurons, and the modulated neural activitymay comprise a neural spike train or neural oscillation. Or, forexample, the excitable cells may comprise cardiomyocytes.

First, a few definitions:

“Threshold amplitude” for a given excitable cell means the minimumamplitude of a single electric field pulse that evokes an actionpotential in the given cell.

“Sub-threshold amplitude” for a given excitable cell means an amplitudethat is less than the threshold amplitude for the given cell.

“Supra-threshold amplitude” for a given excitable cell means anamplitude that is greater than the threshold amplitude for the givencell.

To say that action potentials in a given excitable cell are“time-locked” with a sequence of peaks in an electrical waveform meansthat, for each respective peak in a sequence of peaks, an actionpotential occurs in the given cell after the respective peak and beforethe next peak if any in the sequence.

“Natural band” of a given excitable cell means a range of fundamentalfrequencies such that, for each respective fundamental frequency in therange, a sequence of supra-threshold peaks only at that respectivefundamental frequency would evoke action potentials in the given cellthat are timelocked with the sequence.

“Supra-threshold temporal summation” means a response by an excitablecell, wherein multiple sub-threshold peaks in temporal succession evokean action potential in the cell.

In illustrative implementations, an apparatus drives two isolatedcurrents through biological tissue, in such a manner as to evoke stableaction potential oscillations in excitable cells. In some cases, inorder to evoke these stable action potential oscillations, each of thetwo currents comprises a train of electrical field pulses withsub-threshold amplitude and a frequency higher than the cells' naturalband. The two currents interfere with each other in such a manner as toproduce an amplitude-modulated waveform. This AM waveform has a beatfrequency that falls within the cells' natural frequency band and has asupra-threshold amplitude. The action potentials that are evoked aretime-locked to the sequence of peaks of the AM waveform.

The following 14 paragraphs describe examples in which the excitablecells are neurons.

Electric fields may evoke action potentials or other modulation ofneural activity.

A single pulse of electric field may evoke a single action potential. Inthis case the electric field pulse has supra-threshold amplitude. Thethreshold amplitude, i.e. minimum amplitude, to evoke an actionpotential is inversely dependent on the duration (or width) of thestimulating pulse. If the pulse durations are significantly longer thanthe time constant of the neuron (typically ˜1 ms), a reduction in thepulse duration results in a small linear increase in the threshold.However, if the pulse durations are equal or smaller than the neurontime constant, a reduction in the pulse duration results in a largeexponential increase in the threshold. This principle is known as thestrength-duration response of neurons.

A train of electric field pulses, each with supra-threshold amplitude,may evoke a train of action potentials where each pulse evokes atime-locked action potential. In this case, the electric field peakamplitude needed to evoke a train of action potentials depends on thepulse duration and on the inter-pulse-interval since the neural membranerequires time to recover from an action potential event. (An incompleterecovery of the neural membrane potential results in a larger activationthreshold).

If the electric field train is symmetrical or bio-phasic such assinusoidal, i.e. the pulse width is equal to the inter-pulse-interval;the threshold to evoke a train of action potentials depends simply onthe frequency of the electric field.

If the frequency of the electric field is sufficiently low, the intervalafter each electric field pulse is long enough to allow the neuron tosufficiently repolarize its membrane so the next electric field pulsecan evoke a time-locked action potential.

In this frequency range (the neuron's natural frequency band), the rateof action potentials is directly proportional to the frequency of theelectric field and the threshold to evoke a time-locked action potentialoscillation is inversely proportional to the frequency of the electricfield (higher frequency results in shorter pulse duration and shorterinter-pulse interval).

If the frequency of the electric field train is increased beyond theneuron's natural band, the neuronal membrane does not repolarizesufficiently between electric field pulses leading to the loss of thetime-locked spiking. The actual rate of action potentials in this casemay be significantly lower than the frequency of the electric field.Furthermore, if the electric field frequency is further increasedeventually the neuron will remain depolarized to a level that suppressesany spiking activity.

A different response pattern emerges when the amplitude of the electricfield pulse is lower than the threshold amplitude to evoke an actionpotential, i.e. sub-threshold. In this case, while a single pulse evokesonly sub-threshold depolarization, if the inter-pulse interval issufficiently small, a train of electric field pulses may be summed (orintegrated) by the neuron to evoke supra-threshold, i.e. actionpotential, event. Thus, the neuron's response may comprisesupra-threshold temporal summation, as defined herein. The amplitudethat evokes a single action potential via supra-threshold temporalsummation of sub-threshold pulses depends on the pulse duration and onthe inter-pulse interval (the shorter the electric field inter-pulseinterval the better it is summed up by the neuron). The efficiency ofthe temporal summation of the neuron is determined by itsre-polarization rate, i.e. the rate by which the membrane returns to itsrest potential value following an electrical stimulation.

If the electric field train is symmetrical or bio-phasic such assinusoidal, the neural frequency response has a complex behavior ashigher frequencies result in shorter pulse duration (i.e. higherthreshold due to strength-duration response) but also shorterinter-pulse-interval (lower threshold due to stronger temporalsummation). Overall, the frequency of the sub-threshold electric fieldmust be larger than the natural frequency band to allow sufficienttemporal summation.

A continuous train of sub-threshold electric field pulses may evoke asingle action potential, via supra-threshold temporal summation, buttypically does not evoke a stable time-locked train of action potentialsas there is no stimulation free time for the neuron to repolarize afteran action potential event. Typically, in this case, after the firstaction potentials, the neuron effectively stops to respond to theelectric field and enters a steady-state in which its membrane isslightly depolarized above its rest potential and can respond tointernal or external supra-threshold stimuli. (n some circumstances,there maybe be a narrow amplitude-frequency range in which actionpotential oscillation occurs.)

The amplitude needed to evoke a train of action potentials at a certainnatural frequency depends on the pulse duration (strength-durationresponse), the inter-pulse-interval (temporal summation) and on thestrength of the amplitude modulation (the larger the reduction in theelectric field amplitude, the stronger the repolarization of theneuron).

If the electric field train is symmetrical or bio-phasic such assinusoidal, i.e. the pulse width is equal to the inter-pulse-interval,the threshold to evoke a train of action potentials at a certain naturalfrequency depends on the frequency of the electric field and thestrength of the amplitude modulation.

Similar to the supra-threshold pulse train, the minimum amplitude of anAM waveform which will evoke an action potential oscillation that istimed-locked to the AM waveform is inversely proportional to the AMfrequency of the electric field.

In the case of sub-threshold temporal summation, the neuron experiencesperiodic sub-threshold depolarization at a rate equal to the frequencyof the amplitude modulation.

In illustrative implementations of this invention, an apparatus drivestwo isolated currents in order to cause stable action potentialoscillations of neurons. These stable action potential oscillations areachieved by a train of electric field pulses with a sub-thresholdamplitude and a frequency higher than the neurons' natural band (suchthat the inter-pulse interval is sufficiently small to achievesupra-threshold temporal summation). The two currents interfere withother to produce an amplitude-modulated waveform. The AM waveform has afrequency (sometimes called the beat frequency) in the neurons' naturalband and has a supra-threshold amplitude. The AM waveform allowssufficient repolarization between action potentials. The AM waveformevokes a stable train of time-locked action potentials in the neurons.

The preceding 14 paragraphs describe examples in which the excitablecells are neurons. However, this invention is not limited to modulationof neurons. For example, in some cases, this invention modulatesactivity of cardiomyocytes or of other excitable cells.

When two alternating waves of different frequencies overlap, they createan alternating wave with an effective frequency that is equal to theaverage of the two original frequencies and an amplitude that changesperiodically at a frequency that is equal to the difference of theoriginal frequencies. The amplitude modulation (AM) is due to a periodicchange between a constructive interference (when the two waves arenearly in phase) and a destructive interference (when the two waves arenearly 180 degrees out of phase). The frequency in which the amplitudechanges is sometimes called a beat frequency, an amplitude modulationfrequency, or an envelope frequency. The average of the two originalfrequencies is often called the carrier frequency. The creation of theamplitude modulation can be shown by using the trigonometry sum rule

$2\mspace{11mu} {\sin ( \frac{\alpha + \beta}{2} )}{{\cos ( \frac{\alpha - \beta}{2} )}.}$

Consider the sum of a signal y₁ (t)=A·sin(2πf₁t) and a signaly₂(t)=A·sin(2πf₂t), where f₁>f₂. This sum is equal to

${{y_{1 + 2}( {t,r} )} = {2{A \cdot \cos}\mspace{11mu} {( {2{\pi ( \frac{f_{1} - f_{2}}{2} )}t} ) \cdot \sin}\mspace{11mu} ( {2{\pi ( \frac{f_{1} + f_{2}}{2} )}t} )}},$

that is, a sine function at a frequency

$\frac{f_{1} + f_{2}}{2}$

with an amplitude 2 A that changes periodically by a cosine function ata slow frequency of

$\frac{f_{1} - f_{2}}{2}.$

In some cases, application of two different frequencies to biologicaltissues such as the brain affects a larger variety of frequencies (e.g.harmonics) due to their nonlinear characteristics.

By spatially overlapping two electric fields, the amplitude ofsuperimposed fields is modulated at a rate equal to the differencebetween the electric fields frequencies and at a strength equal to thedifference between the electric field amplitudes. This principle iscalled “interferential summation” and the resulting AM frequency issometimes called the “beat frequency”. The location and spread of the AMfield depends in part on the positioning of the stimulation electrodesrelative to each other.

In illustrative implementations of this example, an apparatus drives twocurrents (such as a first alternating current produced by the first pairof electrodes 101, 104 and a second alternating current produced by thesecond pair of electrodes 102, 103) through a conductive biologicalmedium in such a way as to eliminate or greatly reduce cross-talkbetween the two currents.

FIGS. 2A-2H show neural responses to a time-varying electric field, inillustrative implementations of this invention. The neural responsesshown in FIGS. 2A-2H were evoked by a prototype of this invention, andoccurred in anesthetized mice. In the example shown in FIGS. 2A-2H: (a)a first electrode was positioned 1.5 mm posterior from bregma and 1 mmright of midline; (b) a second electrode was positioned 1.5 mm posteriorfrom bregma and 1.5 mm left of midline; and (c) a patch electrode waspositioned 2.2 to 2.5 mm posterior to bregma and 0.5 mm left of midline.

FIG. 2A shows a neural spike train 201 of a single neuron evoked byamplitude-modulated (AM) waveform formed by the intersection of a 2.00kHz electrical field 203 and a 2.01 kHz electric field 205. FIG. 2Bshows a zoomed view of a single action potential 207 in spike train 201and a zoomed view of the 2.00 and 2.01 kHz electric fields 203, 205.

FIG. 2C shows a neural spike train 210 of a single neuron evoked byamplitude-modulated (AM) waveform 209 that has a 10 Hz beat frequency.FIG. 2D shows a zoomed view of a single action potential 217 in spiketrain 210 and a zoomed view of the AM waveform 209.

FIG. 2E shows a flat response 211 of a single neuron to stimulation by asingle 2 kHz electric field 203. The response is flat in that the fielddoes not evoke any action potential or other change in the neuron. FIG.2F shows a zoomed view of the flat response 211 to the single 2 kHzelectric field 203.

FIG. 2G shows a neural spike train 221 of a single neuron evoked by 10Hz electric field 225. FIG. 2H shows a zoomed view of a single actionpotential 227 in spike train 221 and a zoomed view of the 10 Hz electricfield 225.

In the examples shown in FIGS. 1A-1H: (a) a 2.00 kHz waveform does notevoke any action potential, (b) a 10 Hz electric field evokes a 10 Hzneural spike train; and (c) an AM waveform that is formed by theintersection of 2.00 kHz and 2.01 kHz electric fields and that has abeat frequency of 10 Hz evokes a 10 Hz neural spike train.

In FIGS. 2B, 2D, 2F, and 2H, the zoomed views are horizontally(temporally) zoomed.

In some implementations of this invention, electric fields are appliedvia electrodes. In some other implementations, an electric field isgenerated from an inductive source (e.g. coil) using time-varyingmagnetic field.

In some cases, the current sources produce an electric field pulse. Thepulse may have different shapes (e.g. rectangular, sine, Gaussian, etc.)

In use scenarios that evoke an electric field pulse train, the train maybe of any polarity (e.g. uni-phasic or bi-phasic), symmetrical orasymmetrical. It can also be sinusoidal.

Isolated Currents

Thus, in conventional current drive techniques, the amplitude modulation(AM) of the electric field is not well localized in a tissue (or anyconductive medium) due to crosstalk between the current waveforms. Inconventional current drive techniques, current from one channel isdiverted toward the return path of the second channel leading to astrong amplitude modulation at the electrodes themselves. In the case ofconventional interferential stimulation, this may result in theappearance of a beat frequency near the electrodes and not inside thetissue.

In illustrative implementations of this invention, this problem (ofcurrent leakage) is solved by using a current drive that is anti-phasicor that includes an isolation transformer. The current drive isolatesthe two currents so that current leakage between the two channels isgreatly ameliorated.

In the case of interferential stimulation, this invention enhances thepenetration and localization of an interferential stimulation into deeptissue layers.

More generally, this invention may be beneficial in any circumstance inwhich more than one electric waveform is applied to a conductive medium.In some cases, an isolated current drive provides isolated and localizedstimulation of two or more areas of a tissue. For example, in some usescenarios, one segment of a neural tissue is stimulated with onewaveform (e.g. 10 Hz) and another nearby segment of the same neuraltissue is stimulated with the same or different waveform (e.g. 20 Hz orDC) without interference currents. The neural segments may be a fewmicrometers or millimeters apart as in the case of an invasivestimulator with multiple electrodes or a few centimeters apart as in thecase of noninvasive stimulator.

In illustrative implementations of this invention, an isolated currentdrive is implemented either with an anti-phasic source or with anisolation transformer.

Anti-phasic Source: In the anti-phasic case, a current source drives twodifferent electric waveforms through balanced pairs of electrodes, onewaveform through a first pair of electrodes and a second waveformthrough a second pair of electrodes. At least one electrode pair isanti-phasic, that is, the phase at the first electrode of the pair issubstantially anti-phasic (substantially 180 degrees out-of-phase) fromthe phase at the second electrode of the pair. In some cases, only oneof the electrode pairs is anti-phasic. In other cases, both of the twoelectrode pairs is anti-phasic. In some cases, a ground or referenceelectrode is provided to carry any imbalance currents from the pairedcurrents sources and to prevent charge up of the body relative to earthground. The vast majority (>99%) of the stimulation current created byeach electrode pair does not flow through this ground or referenceelectrode since the current is driven differentially or out of phasewith each other. A benefit of this approach is that most of the currentis not going through the common ground electrodes. This allows multiplecurrent waveforms to flow independently inside the tissue. Thiseliminates (or greatly reduces) crosstalk between the channels andpermits triangulation of the currents through the conductive medium awayfrom the path of current to the ground.

Isolation Transformer: In the isolation transformer case, two currentwaveforms are isolated from each other by connecting the primary wiresof a transformer to a single current source and a ground and connectingthe floating secondary wires of the transformer to two or morestimulating electrodes. This configuration greatly reduces cross-talkbetween the two channels, and thus has a similar effect as ananti-phasic drive. In some cases, a ground or reference electrode isprovided to prevent charge up of the body due to static electricalsources from the environment. In some cases, a conventional currentsource with a ground return electrode creates one stimulus waveform andall other electrodes are isolated by transformers.

Thus, in illustrative implementations of this invention, the twocurrents are isolated from each other, even though the currents areflowing simultaneously through a single conductive medium. This improvesthe efficiency of the modulation of excitable cells (e.g., neurons).

The discussion above refers to electric field but it is valid as well toelectric current or electric potential.

The discussion above refers to a single action potential but it is validalso to a burst of action potentials.

The discussion above to neural cells however it is valid as well toother excitable cells such as muscle cells such as cardiomyocytes and tonerves such as the vestibular nerve.

FIG. 3 shows a conventional IFC device that applies multiple currents toa common conductive load (the load comprises a portion of the body). InFIG. 3, two waveform generators 301, 321 generate voltage waveforms thatcontrol voltage-controlled current sources 302, 322. A first electrodepair 305, 306 and a second electrode pair 325, 326 are each electricallyattached to a common conductive load 340. Current source 302 drives afirst current, and current source 322 drives a second current. Thereturn pathway of each current source is connected to ground. In thisconventional configuration, there is substantial current leakage betweenthe first and second currents.

(In FIG. 3, nodes at which electrical wires connect are indicated by adot. However, this convention is not followed in any other Figure. Forexample, in FIGS. 4A, 4B, 4C, 4D, 8, 9, and 10, nodes at whichelectrical wires connect are not indicated by a dot.)

FIGS. 4A, 4B and 4C each show examples of an anti-phasic current drivefor applying isolated currents to a common conductive load, inillustrative embodiments of this invention. For example, the commonconductive load 440 may comprise biological tissue such as a brain orhead.

In FIGS. 4A, 4B, and 4C, a left-side electrical network comprises (a) afirst pair of electrodes 405, 406 and (b) the circuit componentspositioned to the left (in these Figures) of this first pair ofelectrodes. In FIGS. 4A, 4B, and 4C, a right-side electrical networkcomprises (a) a second pair of electrodes 425, 426 and (b) circuitcomponents positioned to the right (in these Figures) of this secondpair of electrodes.

In FIGS. 4A, 4B and 4C, the right-side network is anti-phasic—that is,the right-side network creates electrical waveforms in an electrode pair(a first waveform at electrode 405 and a second waveform at electrode406), such that these two waveforms have a phase difference that issubstantially equal to 180 degrees.

In FIGS. 4B and 4C, the left-side network is also anti-phasic—that is,the left-side network creates electrical waveforms in an electrode pair(a first waveform at electrode 425 and a second waveform at electrode426), such that these two waveforms have a phase difference that issubstantially equal to 180 degrees.

In FIGS. 4A, 4B and 4C, two waveform generators 401, 421 generatevoltage waveforms that control voltage-controlled current sources (i.e.,current sources 402, 403, 422 in FIG. 4A, and current sources 402, 403,422, 423 in FIG. 4B).

In FIGS. 4A, 4B and 4C, waveform generator 401 generates a voltagewaveform that: (a) is converted to an in-phase current waveform byvoltage-controlled current source 402 and applied to a common conductiveload 440 via electrode 405; and (b) is converted into an anti-phasecurrent waveform by a voltage-controlled current source 406 and appliedto the load 440 via electrode 406. Electrodes 405 and 406 have a phasedifference that is substantially equal to 180 degrees. This phasedifference is achieved by connecting waveform generator 401 to thepositive input of voltage-controlled current source 402 and to thenegative input of a second voltage-controlled current source 403.

In FIG. 4A, waveform generator 421 generates a voltage waveform that isconverted to a current waveform by voltage-controlled current source 422and applied to the common conductive load 440 via a pair of electrodes425, 426.

In FIGS. 4B and 4C, waveform generator 421 generates a voltage waveformthat: (a) is converted to an in-phase current waveform byvoltage-controlled current source 422 and applied to the commonconductive load 440 via electrode 425; and (b) is converted into ananti-phase current waveform by a voltage-controlled current source 426and applied to the load 440 via electrode 426. In FIGS. 4B and 4C,electrodes 425 and 426 have a phase difference that is substantiallyequal to 180 degrees. This phase difference is achieved by connectingwaveform generator 421 to the positive input of voltage-controlledcurrent source 422 and to the negative input of a secondvoltage-controlled current source 423.

In FIG. 4B, a reference electrode 407 is connected to ground 404. Thereference electrode 407 carries any imbalance currents from the pairedcurrents sources and prevents charge up of the load 440 relative toearth ground.

In FIG. 4C, the reference electrode 407 is replaced with four resistors408, 409, 428, 429. Each of these resistors, respectively, shares a nodewith one of the electrodes (405, 406, 425 or 426) at one end of theresistor and is electrically connected to ground at another end of theresistor. The resistors carry any imbalance currents from the pairedcurrents sources and prevent charge up of the load relative to earthground.

The impedance of each of these resistors is preferably at least 10-foldlarger than the impedance of the load 440, in order to limit the currentflow to ground. A variable resistor may be used to adjust the resistanceaccording to the load.

Four resistors 408, 409, 428, 429 are shown in FIG. 4C. However, in somecases, less than four of these resistors are employed. For example, one,two or three of these resistors may be included in the current driveapparatus, in order to carry any imbalance currents from the pairedcurrents sources and to prevent charge up of the load 440 relative toearth ground.

Thus, FIGS. 4A, 4B and 4C all show examples of “anti-phasic” currentdrive.

It is worth noting that a prior art technology is sometimes called“anti-phasic”, even though its structure and function is quitedifferent. As is well known, the position and size of an interferentialregion may be adjusted, by adjusting the relative amplitudes of theoriginal waveforms. Steering the position of the interferential regionin this way is sometimes called “vector rotation”, because it changesthe position vector of the interferential region. In some prior art: (a)the amplitude of one of the original waveforms is increased while theamplitude of the other original waveform is simultaneously decreased,and (b) such reciprocal, simultaneous vector rotation is sometimescalled anti-phasic. However, so-called anti-phasic vector rotation isquite different than an anti-phasic current drive of the presentinvention. Among other things, the vector rotation does not involveapplying current to a load via a pair of electrodes that are inelectrical antiphase to each other.

FIG. 4D shows an example of a current drive that includes an isolationtransformer, and that is configured to apply isolated currents to acommon conductive load, in an illustrative embodiment of this invention.In FIG. 4D, a waveform generator 401 generates a voltage waveform thatis converted to a current waveform by voltage-controlled current source402 and applied to a common conductive load 440 via a pair of electrodes405, 406 through an isolation transformer 451. In this case the primarywires 454, 455 of transformer 451 are connected to the output of thecurrent source and to a ground and the floating secondary wires 452, 453of the transformer 451 are connected to electrodes 405, 406.

In FIG. 4D, waveform generator 421 generates another voltage waveformthat is converted to a current waveform by voltage-controlled currentsource 422. The current is applied to the common conductive load 440 viaa pair of electrodes 425, 426.

More Details

FIGS. 5A, 5B, 5C, 5D, 5E, 5F, 5G, 5H, 5I, 6A, 6B, 6C, 6D, 6E, 6F, 6G,6H, and 6I show measured values of electrical fields in a 2D phantom.The phantom comprised Ag wire electrodes (1 mm cross-section) mounted ina Petri dish with a radius R of 25 mm. The Petri dish was filled with0.9% saline solution. Measurements were taken with two orthogonaldipoles contracted from stainless-steel needle electrodes.

FIG. 5J shows a 2D grayscale amplitude map of a first electrical fieldcreated by passing current between electrode 501 and ground electrode502. FIG. 5A shows a vector map of this first field. FIG. 5D shows a 1Damplitude distribution 510 of this first field along a tangential({circumflex over (t)}) orientation. FIG. 5E shows a 1D amplitudedistribution 511 of this first field along a radial ({circumflex over(r)}) orientation.

FIG. 5K shows a 2D grayscale amplitude map of a second electrical fieldcreated by passing current between electrode 501 and two groundelectrodes 502. FIG. 5B shows a vector map of this second field. FIG. 5Fshows a 1D amplitude distribution 512 of this second field along atangential ({circumflex over (t)}) orientation. FIG. 5G shows a 1Damplitude distribution 513 of this second field along a radial({circumflex over (r)}) orientation.

In the example shown in FIG. 5K (and in FIGS. 5B, 5F and 5G), anisolated current drive is not employed. As a result, there is majorcurrent leakage.

FIG. 5L shows a 2D grayscale amplitude map of a third electrical fieldcreated by passing current between electrode 501 and two groundelectrodes 502. FIG. 5C shows a vector map of this third field. FIG. 5Hshows a 1D amplitude distribution 514 of this third field along atangential ({circumflex over (t)}) orientation. Figure SI shows a 1Damplitude distribution 515 of this third field along a radial({circumflex over (r)}) orientation.

In the example shown in FIG. 5L (and in FIGS. 5C, 5H and 5I), ananti-phasic current drive is employed. As a result, current leakage isgreatly ameliorated, causing the amplitude distribution and vector mapsof the third field to look very similar those of the first field.

In FIGS. 5D, 5E, 5F, 5G, 5H and 5I, the FWHM (full width half maximum ofelectric field distribution) is equal to 0.75 R, 0.2 R, >R, 0.25 R, 0.9R and 0.2 R, respectively, where R is the radius of the Petri dish.

FIG. 6J shows a 2D grayscale amplitude map of a fourth electrical fieldcreated by passing current between electrode 601 and ground electrode605. FIG. 6A shows a vector map of this fourth field. FIG. 6D shows a 1Damplitude distribution 610 of this fourth field along a tangential({circumflex over (t)}) orientation. FIG. 6E shows a 1D amplitudedistribution 611 of this fourth field along a radial ({circumflex over(r)}) orientation.

FIG. 6K shows a 2D grayscale amplitude map of a fifth electrical fieldcreated by passing a first current with a kHz frequency betweenelectrodes 601 and 602 and passing a second current with a different kHzfrequency between electrodes 603 and 604. FIG. 6B shows a vector map ofthis fifth field. FIG. 6F shows a 1D amplitude distribution 612 of thisfifth field along a tangential ({circumflex over (t)}) orientation. FIG.6G shows a 1D amplitude distribution 613 of this fifth field along aradial ({circumflex over (r)}) orientation.

In the example shown in FIG. 6K (and in FIGS. 6B, 6F and 6G), ananti-phasic current drive is employed. As a result, current leakage isgreatly reduced, causing the amplitude distribution and vector maps ofthe fifth field to look very similar those of the fourth field.

FIG. 6L shows a 2D grayscale amplitude map of a sixth electrical fieldcreated by passing a first current with a first between electrode 601and ground electrode 608 and a second current with a different kHzfrequency between electrode 603 and ground electrode 609. FIG. 6C showsa vector map of this sixth field. FIG. 6H shows a 1D amplitudedistribution 614 of this sixth field along a tangential ({circumflexover (t)}) orientation. FIG. 6I shows a 1D amplitude distribution 616 ofthis sixth field along a radial ({circumflex over (r)}) orientation.

In the example shown in FIG. 6L (and in FIGS. 6C, 6H and 6I), ananti-phasic current drive is not employed. As a result, a large amountof current leakage occurs, and the sixth field looks very different thanthe fourth field.

In FIGS. 6D, 6E, 6F, 6G, 6H and 6I, the FWHM (full width half maximum ofelectric field distribution) is equal to 0.5 R, 0.5 R, 0.5 R, R, R and0.6 R, respectively, where R is the radius of the Petri dish.

In some implementations of this invention, it is desirable to positionelectrodes in a side-by-side configuration, rather than a crisscrossconfiguration. FIG. 7 shows an example of side-by-side positioning ofelectrode pairs. In FIG. 7, a first pair of electrodes 702, 703 ispositioned on a scalp of a human head, such that the first pair ofelectrodes is side-by-side with a second pair of electrodes 705, 706.Line segment 701 is between the electrodes of the first pair (i.e., theendpoints of line segment 701 are at electrodes 702 and 703,respectively). Line segment 704 is between the electrodes of the secondpair (i.e., the endpoints of line segment 704 are at electrodes 705 and706, respectively). The two line segments 701, 704 do not intersect eachother and do not intersect plane 722. Line segment 701 lies entirely onone side of plane 722, and line segment 704 lies entirely on the otherside of plane 722.)

In some implementations of this invention, the shape of the AM waveformis modified in order to improve the efficiency by which AM electricfields modulate neural activity. By creating AM electric fields withnon-zero average envelop via a temporal asymmetry or amplitude offset,action potentials may be evoked with lower threshold amplitude.

FIG. 8 shows a conventional zero-mean envelope AM electric field. InFIG. 8, an AM electric field has a zero mean envelope (the sum ofinstantaneous positive and negative envelopes is zero. The AM field 853is formed inside a conductive load 840 by superposition of two zero-meansinusoidal electric waveforms 851, 852 that are generated by waveformgenerators 801, 802. In FIG. 8, waveform generators 801, 802 outputvoltage waveforms that converted to current waveforms viavoltage-controlled current sources 803, 823, respectively. The currentwaveforms are applied to conductive load 840 via electrodes 805, 806,825, 826. The instantaneous mean envelope 863 is zero and is equal tothe instantaneous mean of the top of envelope 861 and the bottom ofenvelope 862.

FIG. 9 shows a non-zero-mean envelope AM waveform formed bysuperposition of two temporally asymmetric waveforms, in an illustrativeimplementation of this invention. In FIG. 9, an AM electric field has anon-zero mean envelope. The AM field 953 is formed inside a conductiveload 940 by superposition of a first sawtooth waveform with slow riseand fast fall and a second sawtooth waveform with a fast rise and a slowfall. The first and second sawtooth waveforms are voltage waveforms thatare generated by waveform generators 901, 921 respectively. In FIG. 9,the amplitude-modulated waveform has an envelope that has a top and abottom. The difference between the voltage at the top and the voltage atthe bottom is not equal to zero during at least part of theamplitude-modulated waveform.

FIG. 10 shows a non-zero-mean envelope AM waveform formed bysuperposition of two waveforms that are amplitude offset from eachother, in an illustrative implementation of this invention. In FIG. 10,an AM electric field has a non-zero mean envelop. The AM field 953 isformed inside a conductive load by superposition of two sinusoidalelectric waveforms 951, 952 with amplitude offset. In some cases, theamplitude offset may be due to D.C. biasing. FIG. 10 shows that bothoriginal waveforms 951 and 952 are amplitude offset. Alternatively, insome cases, the only one of original waveforms 951, 952 is amplitudeoffset. In FIG. 10, the first and second electrical fields are periodic.For each of these fields, the integral of the voltage of the field, overan entire period of the field, is equal to zero relative to earthground.

In both FIGS. 9 and 10, the waveform generators output voltage waveformsthat are converted to current waveforms via voltage-controlled currentsources 903, 923 respectively. The current waveforms are applied toconductive load 940 via electrodes 905, 906, 925, 926. The instantaneousmean envelope 963 is non-zero at most points and is equal to theinstantaneous mean of the top of envelope 961 and the bottom of envelope962.

The schematics in FIGS. 4A-4D and 8-10 are conceptual and simplifiedand, in many cases, do not show all of the components of the electricalnetwork. For example, the network may include switches, amplifiers, andother hardware not shown in the schematics.

FIG. 11 shows hardware components of an anti-phasic current drive. InFIG. 11, waveform generator 1101 outputs a voltage waveform thatcontrols voltage-controlled current sources 1104, 1105, that in turnapply a current to conductive load 1140 via electrodes 1111, 1112.Likewise, waveform generator 1102 outputs a voltage waveform thatcontrols voltage-controlled current sources 1106, 1107, that in turnapply current to conductive load 1140 via electrodes 1114, 1115.

FIG. 12 shows hardware components of a current drive that includes anisolation transformer. In FIG. 12, waveform generator 1101 outputs avoltage waveform that controls voltage-controlled current source 1104,that in turn applies a current to the primary wires of an isolationtransformer 1108. Secondary wires of the transformer apply current toconductive load 1140 via electrodes 1111, 1112. Waveform generator 1102outputs a voltage waveform that controls voltage-controlled currentsource 1106, that in turn applies current to conductive load 1140 viaelectrodes 1114, 1115.

FIG. 13 shows hardware components of a voltage drive that isanti-phasic. In FIG. 13, waveform generator 1101 outputs a voltagewaveform that controls voltage-controlled voltage sources 1154, 1155,that in turn apply a current to conductive load 1140 via electrodes1111, 1112. Likewise, waveform generator 1102 outputs a voltage waveformthat controls voltage-controlled voltage sources 1156, 1157, that inturn apply current to conductive load 1140 via electrodes 1114, 1115.

FIG. 14 shows hardware components of a voltage drive that includes atransformer. In FIG. 14, waveform generator 1101 outputs a voltagewaveform that controls voltage-controlled voltage source 1151, that inturn applies a current to the primary wires of an isolation transformer1108. Secondary wires of the transformer apply current to conductiveload 1140 via electrodes 1111, 1112. Waveform generator 1102 outputs avoltage waveform that controls voltage-controlled voltage source 1106,that in turn applies current to conductive load 1140 via electrodes1114, 1115.

In FIGS. 11, 12, 13, and 14, a computer (e.g., a microcontroller) 1131controls the waveform generators 1101, 1102. The computer 1131 storesand retrieves data from memory device 1135. The computer 1131 interfaceswith other hardware via a wired or fiber optic communication channel(e.g., a USB connection) 1132 or via a wireless module 1133. In somecases, a battery 1140 stores power and provides power to othercomponents of the device. In some cases, one or more voltage regulators1141 regulate voltage supplied to the device.

FIGS. 15A, 15B, 15C, 15D, 15E and 15F show examples of electrodespositioned on neuromodulation targets, in illustrative implementationsof this invention. FIG. 15A shows a set of four electrodes 1501positioned on the scalp 1503 of a head. FIG. 15B shows a set of foursubdural electrodes 1511 positioned near a brain. FIG. 15C shows aneural probe 1521 inserted deep into a brain. FIG. 15D shows the tip1523 of probe 1521. The probe tip includes four electrodes 1525, 1526,1527, 1528. FIG. 15E shows a set of four transcutaneous electrodes 1531positioned on the scalp of a head. FIG. 15F shows a set of fourelectrodes 1543 positioned on a nerve 1541.

In many embodiments of this invention, the electric fields generated bythe first and second current channels, and any AM waveform created byinterference of these electric fields, are periodic. Alternatively, oneor more of these fields is aperiodic and the AM waveform created bytheir interference is aperiodic.

In illustrative embodiments, this invention may be used to advantagewith implantable stimulating electrodes, such as electrodes 1525, 1526,1527, 1528 shown in FIGS. 15D and 15E. In some embodiments of thisinvention: (a) implantable electrodes are implanted in a brain andcreate a high amplitude region that is path-connected and consists onlyof spatial points in the brain at which the largest envelope amplitudeoccurs; and (b) the minimum distance between the high amplitude regionand the electrodes in the first and second pairs of electrodes is atleast 0.9 times the minimum distance between the first and second pairsof electrodes.

Computers

In exemplary implementations of this invention, one or more electroniccomputers (e.g. 1131) are programmed and specially adapted: (1) tocontrol the operation of, or interface with, hardware components of acurrent drive or voltage drive, including any waveform generators; (2)to perform any other calculation, computation, program, algorithm,computer function or computer task described or implied above; (3) toreceive signals indicative of human input; (4) to output signals forcontrolling transducers for outputting information in human perceivableformat; and (5) to process data, to perform computations, to execute anyalgorithm or software, and to control the read or write of data to andfrom memory devices. The one or more computers may be in any position orpositions within or outside of the device. For example, in some cases(a) at least one computer is housed in or together with other componentsof the device, and (b) at least one computer is remote from othercomponents of the device. The one or more computers are connected toeach other or to other components in the device either: (a) wirelessly,(b) by wired connection, (c) by fiber-optic link, or (d) by acombination of wired, wireless or fiber optic links.

In exemplary implementations, one or more computers are programmed toperform any and all calculations, computations, programs, algorithms,computer functions and computer tasks described or implied above. Forexample, in some cases: (a) a machine-accessible medium has instructionsencoded thereon that specify steps in a software program; and (b) thecomputer accesses the instructions encoded on the machine-accessiblemedium, in order to determine steps to execute in the program. Inexemplary implementations, the machine-accessible medium comprises atangible non-transitory medium. In some cases, the machine-accessiblemedium comprises (a) a memory unit or (b) an auxiliary memory storagedevice. For example, in some cases, a control unit in a computer fetchesthe instructions from memory.

In illustrative implementations, one or more computers execute programsaccording to instructions encoded in one or more tangible,non-transitory, computer-readable media. For example, in some cases,these instructions comprise instructions for a computer to perform anycalculation, computation, program, algorithm, computer function orcomputer task described or implied above. For example, in some cases,instructions encoded in a tangible, non-transitory, computer-accessiblemedium comprise instructions for a computer to: 1) to control theoperation of, or interface with, hardware components of a current driveor voltage drive, including any waveform generators; (2) to perform anyother calculation, computation, program, algorithm, computer function orcomputer task described or implied above; (3) to receive signalsindicative of human input; (4) to output signals for controllingtransducers for outputting information in human perceivable format; and(5) to process data, to perform computations, to execute any algorithmor software, and to control the read or write of data to and from memorydevices.

Definitions

The terms “a” and “an”, when modifying a noun, do not imply that onlyone of the noun exists.

To say that an electric network is “anti-phasic” means that the networkincludes a first electrode and a second electrode and is configured tosimultaneously create a first electrical waveform at the first electrodeand a second electrical waveform at the second electrode, the firstwaveform having a first phase and the second waveform having a secondphase, such that the difference between the first and second phases issubstantially equal to 180 degrees.

The term “comprise” (and grammatical variations thereof) shall beconstrued as if followed by “without limitation”. If A comprises B, thenA includes B and may include other things.

The term “computer” includes any computational device that performslogical and arithmetic operations. For example, in some cases, a“computer” comprises an electronic computational device, such as anintegrated circuit, a microprocessor, a mobile computing device, alaptop computer, a tablet computer, a personal computer, or a mainframecomputer. In some cases, a “computer” comprises: (a) a centralprocessing unit, (b) an ALU (arithmetic logic unit), (c) a memory unit,and (d) a control unit that controls actions of other components of thecomputer so that encoded steps of a program are executed in a sequence.In some cases, a “computer” also includes peripheral units including anauxiliary memory storage device (e.g., a disk drive or flash memory), orincludes signal processing circuitry. However, a human is not a“computer”, as that term is used herein.

“Defined Term” means a term or phrase that is set forth in quotationmarks in this Definitions section.

For an event to occur “during” a time period, it is not necessary thatthe event occur throughout the entire time period. For example, an eventthat occurs during only a portion of a given time period occurs “during”the given time period.

The term “e.g.” means for example.

The “envelope amplitude” of an amplitude-modulated waveform is equal tothe peak amplitude of a signal, which signal is the top of the envelopeof the amplitude-modulated waveform.

The fact that an “example” or multiple examples of something are givendoes not imply that they are the only instances of that thing. Anexample (or a group of examples) is merely a non-exhaustive andnon-limiting illustration.

Unless the context clearly indicates otherwise: (1) a phrase thatincludes “a first” thing and “a second” thing does not imply an order ofthe two things (or that there are only two of the things); and (2) sucha phrase is simply a way of identifying the two things, respectively, sothat they each may be referred to later with specificity (e.g., byreferring to “the first” thing and “the second” thing later). Forexample, unless the context clearly indicates otherwise, if an equationhas a first term and a second term, then the equation may (or may not)have more than two terms, and the first term may occur before or afterthe second term in the equation. A phrase that includes a “third” thing,a “fourth” thing and so on shall be construed in like manner.

“For instance” means for example.

“Frequency” means fundamental frequency, unless the context explicitlyindicates otherwise.

As used herein, to say that a thing (such as an object, event or fact)is “given” carries no implication regarding whether the thing isassumed, known or existing. As used herein, “given” simply identifies athing (such as an object, event or fact), so that the thing may bereferred to later with specificity.

“Ground” means electrical ground in an electrical circuit.

“Herein” means in this document, including text, specification, claims,abstract, and drawings.

As used herein: (1) “implementation” means an implementation of thisinvention; (2) “embodiment” means an embodiment of this invention; (3)“case” means an implementation of this invention; and (4) “use scenario”means a use scenario of this invention.

The term “include” (and grammatical variations thereof) shall beconstrued as if followed by “without limitation”.

“Line segment” means a straight line segment.

“Load” means an electrical load in an electrical circuit.

An “output terminal” of a current source means a terminal from which, orinto which, current created by the current source flows.

“Orthographic” refers to a projection in which each line of projectionis perpendicular to a plane onto which the projection is being made.

“Node” means an electrical node in an electrical circuit.

To say that X is “out of” Y and Z means that X is a member of a set thatconsists of Y and Z.

The term “or” is inclusive, not exclusive. For example A or B is true ifA is true, or B is true, or both A or B are true. Also, for example, acalculation of A or B means a calculation of A, or a calculation of B,or a calculation of A and B.

As used herein, “parameter” means a variable. For example: (a) ify=f(x), then both x and y are parameters; and (b) if z=f(x(t), y(t)),then t, x, y and z are parameters. A parameter may represent a physicalquantity, such as pressure, temperature, or delay time.

A parenthesis is simply to make text easier to read, by indicating agrouping of words. A parenthesis does not mean that the parentheticalmaterial is optional or may be ignored.

The term “path-connected” means path-connected, in the topological senseof the term.

As used herein, the term “set” does not include a group with noelements. Mentioning a first set and a second set does not, in and ofitself, create any implication regarding whether or not the first andsecond sets overlap (that is, intersect). A set has one or moreelements. As used herein, the phrase “set of ______”, where the blank isfilled in by any plural noun, means a “set of one or more ______”. Forexample, a set of pencils means a set of one or more pencils.

To say that a first pair of electrodes and a second pair of electrodesare positioned “side-by-side” means that, for a first line segment thatjoins the electrodes of the first pair and a second line segment thatjoins the electrodes of the second pair, a geometric plane exists suchthat (i) the first line segment is positioned entirely on one side ofthe plane; (ii) the second line segment is positioned entirely on theother side of the plane; and (ii) neither the first line segment nor thesecond line segment intersect the plane.

“Some” means one or more.

To “stimulate” means to apply a stimulus or stimuli. The words“stimulate” and “stimulus” carry no implication regarding whether or howthe person or thing being stimulated responds. For example, in somecases, a “stimulus” may evoke activity, suppress activity, or evoke noresponse.

As used herein, a “subset” of a set consists of less than all of theelements of the set.

“Substantially” means at least ten percent. For example: (a) 112 issubstantially larger than 100; and (b) 108 is not substantially largerthan 100.

To say that a first electric field and a second electric field are“substantially isolated from each other”—in a context where the firstelectric field is created by a first pair of electrodes, the secondelectric field is created by a second pair of electrodes, and the firstand second pairs of electrodes are electrically connected to a commonconductive load—means that a first ratio and a second ratio are eachless than or equal to 0.07, where: (a) the first pair of electrodescomprises a first electrode and a second electrode; (b) the first ratiois a ratio of the magnitude of the highest magnitude frequency componentof a second voltage to the magnitude of the highest magnitude frequencycomponent of a first voltage; (c) the second pair of electrodescomprises a third electrode and a fourth electrode; (d) the second ratiois a ratio of the magnitude of the highest magnitude frequency componentof a fourth voltage to the magnitude of the highest magnitude frequencycomponent of a third voltage; (e) the first voltage is the voltageacross the conductive load from the first electrode to the secondelectrode that is attributable to the first electric field; (f) thesecond voltage is the voltage across the conductive load from the firstelectrode to the second electrode that is attributable to the secondelectric field; (g) the third voltage is the voltage across theconductive load from the third electrode to the fourth electrode that isattributable to the second electric field; and (h) the fourth voltage isthe voltage across the conductive load from the third electrode to thefourth electrode that is attributable to the second electric field.

The term “such as” means for example.

To say that a first electric field and second electric field are“temporally asymmetric means that: (a) the first electrical field is aperiodic waveform that has a first rise time and a first fall time; (b)the second electrical field is a periodic waveform that has a secondrise time and a second fall time; and (c) either: (i) the first risetime is longer than the first fall time and the second rise time isshorter than the second fall time, or (ii) the first rise time isshorter than the first fall time and the second rise time is longer thanthe second fall time.

The term “waveform” carries no implication regarding whether thewaveform is periodic. A waveform may be either periodic or aperiodic.

Except to the extent that the context clearly requires otherwise, ifsteps in a method are described herein, then the method includesvariations in which: (1) steps in the method occur in any order orsequence, including any order or sequence different than that described;(2) any step or steps in the method occurs more than once; (3) differentsteps, out of the steps in the method, occur a different number of timesduring the method, (4) any combination of steps in the method is done inparallel or serially; (5) any step or steps in the method is performediteratively; (6) a given step in the method is applied to the same thingeach time that the given step occurs or is applied to different thingseach time that the given step occurs; or (7) the method includes othersteps, in addition to the steps described.

This Definitions section shall, in all cases, control over and overrideany other definition of the Defined Terms. For example, the definitionsof Defined Terms set forth in this Definitions section override commonusage or any external dictionary. If a given term is explicitly orimplicitly defined in this document, then that definition shall becontrolling, and shall override any definition of the given term arisingfrom any source (e.g., a dictionary or common usage) that is external tothis document. If this document provides clarification regarding themeaning of a particular term, then that clarification shall, to theextent applicable, override any definition of the given term arisingfrom any source (e.g., a dictionary or common usage) that is external tothis document. To the extent that any term or phrase is defined orclarified herein, such definition or clarification applies to anygrammatical variation of such term or phrase, taking into account thedifference in grammatical form. For example, the grammatical variationsinclude noun, verb, participle, adjective, and possessive forms, anddifferent declensions, and different tenses. In each case described inthis paragraph, the Applicant or Applicants are acting as his, her, itsor their own lexicographer.

Variations

This invention may be implemented in many different ways. Here are somenon-limiting examples:

In one aspect, this invention is a method comprising: (a) a firstelectrical network creating a first electric field between electrodes ina first pair of electrodes; and (b) a second electrical network creatinga second electric field between electrodes in a second pair ofelectrodes, such that (i) the first and second electric fieldsconstructively and destructively interfere with each other to create anamplitude-modulated waveform and (ii) the largest envelope amplitude ofthe amplitude-modulated waveform occurs in a brain; wherein, duringsteps (a) and (b) above, the first and second electrode pairs areelectrically connected to the brain. In some cases, the first electrodepair and second electrode pair are positioned side-by-side. In somecases: (a) the amplitude modulated waveform has an envelope amplitude;and (b) the first electrode pair and second electrode pair arepositioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the brain, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases, the region spatially coincides with cortical tissue ofthe brain. In some cases, the region spatially coincides withsubcortical tissue of the brain. In some cases: (a) the amplitudemodulated waveform has an envelope amplitude; (b) the greatest magnitudeof the envelope amplitude occurs in a spatial position in the brain; (c)a volume exists, which volume consists of only those points at which themagnitude of the envelope amplitude is equal to at least 50% of thegreatest magnitude; and (d) this volume coincides with both cortical andsubcortical tissue of the brain. In some cases: (a) the first electricalnetwork comprises a first waveform generator, a first set of one or moredependent current sources, and a first pair of electrodes, (b) the firstwaveform generator controls the first set of current sources, (c) thefirst set of current sources creates an electrical current that flowsthrough the first pair of electrodes; (d) the second electrical networkcomprises a second waveform generator, a second set of one or moredependent current sources, and a second pair of electrodes, (e) thesecond waveform generator controls the second set of current sources,and (f) the second set of current sources creates an electrical currentthat flows through the second pair of electrodes. In some cases, atleast one of the first and second electrical networks is anti-phasic. Insome cases: (a) the first set of current sources comprises a firstcurrent source and a second current source; (b) a positive inputterminal of the first current source is electrically connected to thefirst waveform generator and a negative input terminal of the firstcurrent source is electrically connected to ground; and (c) a negativeinput terminal of the second current source is electrically connected tothe first waveform generator and a positive input terminal of the secondcurrent source is electrically connected to ground. In some cases: (a)the first and second pairs of electrodes are implanted inside the brain;and (b) the minimum distance between the region and the electrodes inthe first and second pairs of electrodes is at least 0.9 times theminimum distance between the first and second pairs of electrodes. Insome cases: (a) a resistor is connected to ground; and (c) an electrode,out of the first and second pairs of electrodes, share a common node. Insome cases: the method includes an additional electrode that itconfigured to be electrically connected to both the load and groundwhile the first and second electrode pairs are electrically connected tothe load. In some cases: (a) a given electrical network, out of thefirst and second networks, includes a transformer; (b) a secondary wireof the transformer is electrically connected to an electrode in thefirst pair of electrodes; (c) another secondary wire of the transformeris electrically connected to another electrode in the first pair ofelectrodes; (d) the first set of current sources includes a givencurrent source; (e) a primary wire of the transformer is connected anoutput terminal of the given current source; and (f) another primarywire of the transformer is connected another output terminal of the givecurrent source. In some cases, the amplitude-modulated waveform entrainsneurons in a portion of the brain. In some cases: (a) theamplitude-modulated waveform includes a sequence of peaks; and (b) theamplitude-modulated waveform stimulates neurons in at least a portion ofthe brain such that the neurons undergo a sequence of action potentialsthat is time-locked to the sequence of peaks. In some cases: (a) theamplitude-modulated waveform has an envelope that has a top and abottom; and (b) the difference between the voltage at the top and thevoltage at the bottom is not equal to zero during at least part of theamplitude-modulated waveform. In some cases: (a) a given electricalfield, out of the first and second electrical fields, is periodic; and(b) the integral of the voltage of the given electrical field, over anentire period of the electrical field, is equal to zero relative toearth ground. In some cases, the first and second electric fields aretemporally asymmetric. In some cases, a given current source, out of thefirst and second sets of current sources, has an internal resistancegreater than one mega-ohm in the compliance voltage range of the givencurrent source. In some cases, the first and second electric fields areaperiodic. In some cases, the first and second electrical fields aresubstantially isolated from each other even though (i) the first andsecond pairs of electrodes are electrically connected to the brain and(ii) each of the fields extends through all of the brain. Each of thecases described above in this paragraph is an example of the methoddescribed in the first sentence of this paragraph, and is also anexample of an embodiment of this invention that may be combined withother embodiments of this invention.

In another aspect, this invention is an apparatus comprising: (a) afirst electrical network for creating a first electric field betweenelectrodes in a first pair of electrodes; and (b) a second electricalnetwork for creating a second electric field between electrodes in asecond pair of electrodes, such that (i) when the first and second pairsof electrodes are electrically connected to a brain, the first andsecond electric fields constructively and destructively interfere witheach other to create an amplitude-modulated waveform, and (ii) thelargest envelope amplitude of the amplitude-modulated waveform occurs inthe brain. In some cases, the first electrode pair and second electrodepair are configured to be positioned side-by-side. In some cases, thefirst electrode pair and second electrode pair are configured to bepositioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the brain, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases, the region spatially coincides with cortical tissue ofthe brain. In some cases, the region spatially coincides withsubcortical tissue of the brain. In some cases: (a) the amplitudemodulated waveform has an envelope amplitude; (b) the greatest magnitudeof the envelope amplitude occurs in a spatial position in the brain; (c)a volume exists, which volume consists of only those points at which themagnitude of the envelope amplitude is equal to at least 50% of thegreatest magnitude; and (d) this volume coincides with both cortical andsubcortical tissue of the brain. In some cases: (a) the first electricalnetwork comprises a first waveform generator, a first set of one or moredependent current sources, and a first pair of electrodes, (b) the firstwaveform generator is configured to control the first set of currentsources, (c) the first set of current sources is configured to createone or more electrical currents such that the first pair of electrodescreates the first electrical field, (d) the second electrical networkcomprises a second waveform generator, a second set of one or moredependent current sources, and a second pair of electrodes, (e) thesecond waveform generator is configured to control the second set ofcurrent sources, and (f) the second set of current sources is configuredto create one or more electrical currents such that the second pair ofelectrodes creates the second electrical field. In some cases, at leastone of the first and second electrical networks is anti-phasic. 30. Insome cases: (a) the first set of current sources comprises a firstcurrent source and a second current source; b) a positive input terminalof the first current source is electrically connected to the firstwaveform generator and a negative input terminal of the first currentsource is electrically connected to ground; and (c) a negative inputterminal of the second current source is electrically connected to thefirst waveform generator and a positive input terminal of the secondcurrent source is electrically connected to ground. In some cases, thefirst and second pairs of electrodes are configured to be implantedinside the brain, such that, at a time when the first and second pairsof electrodes are implanted inside the brain, the minimum distancebetween the region and the electrodes in the first and second pairs ofelectrodes is at least 0.9 times the minimum distance between the firstand second pairs of electrodes. In some cases: (a) a resistor isconnected to ground; and (b) an electrode, out of the first and secondpairs of electrodes, share a common node. In some cases, the apparatusincludes an additional electrode that it configured to be electricallyconnected to both the load and ground while the first and secondelectrode pairs are electrically connected to the load. In some cases:(a) a given electrical network, out of the first and second networks,includes a transformer; (b) a secondary wire of the transformer iselectrically connected to an electrode in the first pair of electrodes;(c) another secondary wire of the transformer is electrically connectedto another electrode in the first pair of electrodes; (d) the first setof current sources includes a given current source; (e) a primary wireof the transformer is connected an output terminal of the given currentsource; and (f) another primary wire of the transformer is connectedanother output terminal of the give current source. In some cases, theamplitude-modulated waveform entrains neurons in a portion of the brain.In some cases, (a) the amplitude-modulated waveform includes a sequenceof peaks; and (b) the amplitude-modulated waveform stimulates neurons inat least a portion of the brain such that the neurons undergo a sequenceof action potentials that is time-locked to the sequence of peaks. Insome cases: (a) the amplitude-modulated waveform has an envelope thathas a top and a bottom; and (b) the difference between the voltage atthe top and the voltage at the bottom is not equal to zero during atleast part of the amplitude-modulated waveform. In some cases: (a) agiven electrical field, out of the first and second electrical fields,is periodic; and (b) the integral of the voltage of the given electricalfield, over an entire period of the electrical field, is equal to zerorelative to earth ground. In some cases, the first and second electricfields are temporally asymmetric. In some cases, a given current source,out of the first and second sets of current sources, has an internalresistance greater than one mega-ohm in the compliance voltage range ofthe given current source. In some cases, the first and second electricfields are aperiodic. In some cases, when the first and second pairs ofelectrodes are electrically connected to the brain, the first and secondelectrical fields are substantially isolated from each other even thougheach of the fields extends through all of the brain. Each of the casesdescribed above in this paragraph is an example of the apparatusdescribed in the first sentence of this paragraph, and is also anexample of an embodiment of this invention that may be combined withother embodiments of this invention.

In another aspect, this invention is a method comprising: (a) a firstelectrical network creating a first electrical field between electrodesin a first pair of electrodes; and (b) a second electrical networkcreating a second electrical field between electrodes in a second pairof electrodes, the first and second pairs of electrodes beingelectrically connected to a common conductive load; wherein (i) at leastone of the electrical networks is anti-phasic, (ii) the first electricalnetwork comprises a first waveform generator, a first set of one or moredependent current sources, and a first pair of electrodes, (iii) thefirst waveform generator controls the first set of current sources, (iv)the first set of current sources creates an electrical current thatflows through the first pair of electrodes; (v) the second electricalnetwork comprises a second waveform generator, a second set of one ormore dependent current sources, and a second pair of electrodes, (vi)the second waveform generator controls the second set of currentsources, and (vii) the second set of current sources creates anelectrical current that flows through the second pair of electrodes. Insome cases: (a) the first set of current sources comprises a firstcurrent source and a second current source; (b) a positive inputterminal of the first current source is electrically connected to thefirst waveform generator and a negative input terminal of the firstcurrent source is electrically connected to ground; and (c) a negativeinput terminal of the second current source is electrically connected tothe first waveform generator and a positive input terminal of the secondcurrent source is electrically connected to ground. In some cases: (a)the second set of current sources comprises a third current source and afourth current source; (b) a positive input terminal of the thirdcurrent source is electrically connected to the second waveformgenerator and a negative input terminal of the third current source iselectrically connected to ground; and (c) a negative input terminal ofthe fourth current source is electrically connected to the secondwaveform generator and a positive input terminal of the fourth currentsource is electrically connected to ground. In some cases: a) a resistoris connected to ground; and (b) an electrode, out of the first andsecond pairs of electrodes, share a common node. In some cases, thefirst and second sets of current sources comprise voltage-controlledcurrent sources. In some cases, a given current source, out of the firstand second sets of current sources, has an internal resistance greaterthan one mega-ohm in the compliance voltage range of the given currentsource. In some cases, the first and second electric fields areaperiodic. In some cases, the first and second electrical fields aresubstantially isolated from each other even though (i) the first andsecond electrical pairs are electrically connected to the conductiveload, and (ii) each of the fields extends through all of the conductiveload. In some cases, the common conductive load includes a brain. Insome cases: (a) neurons in a first region of the brain entrain to thefirst electrical field and not to the second electrical field; and (b)neurons in the second region of the brain entrain to the secondelectrical field and not to the first electrical field. In some cases:(a) the first and second electric fields constructively anddestructively interfere with each other to create an amplitude-modulatedwaveform in the brain; and (b) at least some neurons in the brainentrain to the amplitude-modulated waveform. Each of the cases describedabove in this paragraph is an example of the method described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

In another aspect, this invention is an apparatus comprising: (a) afirst electrical network for creating a first electrical field betweenelectrodes in a first pair of electrodes; and (b) a second electricalnetwork for creating a second electrical field between electrodes in asecond pair of electrodes, the first and second pairs of electrodesbeing configured to be electrically connected to a common conductiveload; wherein (i) at least one of the electrical networks isanti-phasic, (ii) the first electrical network comprises a firstwaveform generator, a first set of one or more dependent currentsources, and a first pair of electrodes, (iii) the first waveformgenerator is configured to control the first set of current sources,(iv) the first set of current sources is configured to create anelectrical current that flows through the first pair of electrodes, (v)the second electrical network comprises a second waveform generator, asecond set of one or more dependent current sources, and a second pairof electrodes, (vi) the second waveform generator is configured tocontrol the second set of current sources, and (vii) the second set ofcurrent sources is configured to create an electrical current that flowsthrough the second pair of electrodes. In some cases: (a) the first setof current sources comprises a first current source and a second currentsource; (b) a positive input terminal of the first current source iselectrically connected to the first waveform generator and a negativeinput terminal of the first current source is electrically connected toground; and (c) a negative input terminal of the second current sourceis electrically connected to the first waveform generator and a positiveinput terminal of the second current source is electrically connected toground. In some cases: (a) the second set of current sources comprises athird current source and a fourth current source; (b) a positive inputterminal of the third current source is electrically connected to thesecond waveform generator and a negative input terminal of the thirdcurrent source is electrically connected to ground; and (c) a negativeinput terminal of the fourth current source is electrically connected tothe second waveform generator and a positive input terminal of thefourth current source is electrically connected to ground. In somecases: a) a resistor is connected to ground; and (b) an electrode, outof the first and second pairs of electrodes, share a common node. Insome cases, the first and second sets of current sources comprisevoltage-controlled current sources. In some cases, a given currentsource, out of the first and second sets of current sources, has aninternal resistance greater than one mega-ohm in the compliance voltagerange of the given current source In some cases, the first and secondelectric fields are aperiodic. In some cases, when the first and secondpairs of electrodes are electrically connected to the conductive load,the first and second electrical fields are substantially isolated fromeach other even though each of the fields extends through all of theconductive load. In some cases, the common conductive load includes abrain. In some cases, when the first and second pairs of electrodes areelectrically connected to the brain: (a) neurons in a first region ofthe brain entrain to the first electrical field and not to the secondelectrical field; and (b) neurons in the second region of the brainentrain to the second electrical field and not to the first electricalfield. In some cases, when the first and second pairs of electrodes areelectrically connected to the brain: (a) the first and second electricfields constructively and destructively interfere with each other tocreate an amplitude-modulated waveform in the brain; and (b) at leastsome neurons in the brain entrain to the amplitude-modulated waveform.Each of the cases described above in this paragraph is an example of theapparatus described in the first sentence of this paragraph, and is alsoan example of an embodiment of this invention that may be combined withother embodiments of this invention.

In another aspect, this invention is a method comprising: (a) a firstelectrical network creating a first electric field between electrodes ina first pair of electrodes; and (b) a second electrical network creatinga second electric field between electrodes in a second pair ofelectrodes, such that (i) the first and second electric fieldsconstructively and destructively interfere with each other to create anamplitude-modulated waveform and (ii) the largest envelope amplitude ofthe amplitude-modulated waveform occurs in a heart; wherein, duringsteps (a) and (b) of this sentence, the first and second electrode pairsare electrically connected to the heart. In some cases, the firstelectrode pair and second electrode pair are positioned side-by-side. Insome cases: (a) the amplitude modulated waveform has an envelopeamplitude; and (b) the first electrode pair and second electrode pairare positioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the heart, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases: (a) the first electrical network comprises a firstwaveform generator, a first set of one or more dependent currentsources, and a first pair of electrodes, (b) the first waveformgenerator controls the first set of current sources, (c) the first setof current sources creates an electrical current that flows through thefirst pair of electrodes; (d) the second electrical network comprises asecond waveform generator, a second set of one or more dependent currentsources, and a second pair of electrodes, (e) the second waveformgenerator controls the second set of current sources, and (f) the secondset of current sources creates an electrical current that flows throughthe second pair of electrodes. In some cases, at least one of the firstand second electrical networks is anti-phasic. In some cases: (a) thefirst set of current sources comprises a first current source and asecond current source; (b) a positive input terminal of the firstcurrent source is electrically connected to the first waveform generatorand a negative input terminal of the first current source iselectrically connected to ground; and (c) a negative input terminal ofthe second current source is electrically connected to the firstwaveform generator and a positive input terminal of the second currentsource is electrically connected to ground. Each of the cases describedabove in this paragraph is an example of the method described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

In another aspect, this invention is an apparatus comprising: (a) afirst electrical network for creating a first electric field betweenelectrodes in a first pair of electrodes; and (b) a second electricalnetwork for creating a second electric field between electrodes in asecond pair of electrodes, such that (i) when the first and second pairsof electrodes are electrically connected to a heart, the first andsecond electric fields constructively and destructively interfere witheach other to create an amplitude-modulated waveform, and (ii) thelargest envelope amplitude of the amplitude-modulated waveform occurs inthe heart. In some cases, the first electrode pair and second electrodepair are configured to be positioned side-by-side. In some cases, thefirst electrode pair and second electrode pair are configured to bepositioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the heart, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases: (a) the first electrical network comprises a firstwaveform generator, a first set of one or more dependent currentsources, and a first pair of electrodes, (b) the first waveformgenerator is configured to control the first set of current sources, (c)the first set of current sources is configured to create one or moreelectrical currents such that the first pair of electrodes creates thefirst electrical field, (d) the second electrical network comprises asecond waveform generator, a second set of one or more dependent currentsources, and a second pair of electrodes, (e) the second waveformgenerator is configured to control the second set of current sources,and (f) the second set of current sources is configured to create one ormore electrical currents such that the second pair of electrodes createsthe second electrical field. In some cases, at least one of the firstand second electrical networks is anti-phasic. In some cases: (a) thefirst set of current sources comprises a first current source and asecond current source; (b) a positive input terminal of the firstcurrent source is electrically connected to the first waveform generatorand a negative input terminal of the first current source iselectrically connected to ground; and (c) a negative input terminal ofthe second current source is electrically connected to the firstwaveform generator and a positive input terminal of the second currentsource is electrically connected to ground. Each of the cases describedabove in this paragraph is an example of the apparatus described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

In another aspect, this invention is a method comprising: (a) a firstelectrical network creating a first electric field between electrodes ina first pair of electrodes; and (b) a second electrical network creatinga second electric field between electrodes in a second pair ofelectrodes, such that (i) the first and second electric fieldsconstructively and destructively interfere with each other to create anamplitude-modulated waveform and (ii) the largest envelope amplitude ofthe amplitude-modulated waveform occurs in a nerve; wherein, duringsteps (a) and (b) of this claim 1, the first and second electrode pairsare electrically connected to the nerve. In some cases, the firstelectrode pair and second electrode pair are positioned side-by-side. Insome cases: (a) the amplitude modulated waveform has an envelopeamplitude; and (b) the first electrode pair and second electrode pairare positioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the nerve, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases: (a) the first electrical network comprises a firstwaveform generator, a first set of one or more dependent currentsources, and a first pair of electrodes, (b) the first waveformgenerator controls the first set of current sources, (c) the first setof current sources creates an electrical current that flows through thefirst pair of electrodes; (d) the second electrical network comprises asecond waveform generator, a second set of one or more dependent currentsources, and a second pair of electrodes, (e) the second waveformgenerator controls the second set of current sources, and (f) the secondset of current sources creates an electrical current that flows throughthe second pair of electrodes. In some cases, at least one of the firstand second electrical networks is anti-phasic. In some cases: (a) thefirst set of current sources comprises a first current source and asecond current source; (b) a positive input terminal of the firstcurrent source is electrically connected to the first waveform generatorand a negative input terminal of the first current source iselectrically connected to ground; and (c) a negative input terminal ofthe second current source is electrically connected to the firstwaveform generator and a positive input terminal of the second currentsource is electrically connected to ground. Each of the cases describedabove in this paragraph is an example of the method described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

In another aspect, this invention is an apparatus comprising: (a) afirst electrical network for creating a first electric field betweenelectrodes in a first pair of electrodes; and (b) a second electricalnetwork for creating a second electric field between electrodes in asecond pair of electrodes, such that (i) when the first and second pairsof electrodes are electrically connected to a nerve, the first andsecond electric fields constructively and destructively interfere witheach other to create an amplitude-modulated waveform, and (ii) thelargest envelope amplitude of the amplitude-modulated waveform occurs inthe nerve. In some cases, the first electrode pair and second electrodepair are configured to be positioned side-by-side. In some cases, thefirst electrode pair and second electrode pair are configured to bepositioned such that, at a given time, the largest magnitude of theenvelope amplitude occurs in only one region of the nerve, which regionis path-connected and consists only of those points at which themagnitude of the envelope amplitude is equal to the largest magnitude.In some cases: (a) the first electrical network comprises a firstwaveform generator, a first set of one or more dependent currentsources, and a first pair of electrodes, (b) the first waveformgenerator is configured to control the first set of current sources, (c)the first set of current sources is configured to create one or moreelectrical currents such that the first pair of electrodes creates thefirst electrical field, (d) the second electrical network comprises asecond waveform generator, a second set of one or more dependent currentsources, and a second pair of electrodes, (e) the second waveformgenerator is configured to control the second set of current sources,and (f) the second set of current sources is configured to create one ormore electrical currents such that the second pair of electrodes createsthe second electrical field. In some cases, at least one of the firstand second electrical networks is anti-phasic. In some cases: (a) thefirst set of current sources comprises a first current source and asecond current source; (b) a positive input terminal of the firstcurrent source is electrically connected to the first waveform generatorand a negative input terminal of the first current source iselectrically connected to ground; and (c) a negative input terminal ofthe second current source is electrically connected to the firstwaveform generator and a positive input terminal of the second currentsource is electrically connected to ground. Each of the cases describedabove in this paragraph is an example of the apparatus described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

The above description (including without limitation any attacheddrawings and figures) describes illustrative implementations of theinvention. However, the invention may be implemented in other ways. Themethods and apparatus which are described above are merely illustrativeapplications of the principles of the invention. Other arrangements,methods, modifications, and substitutions by one of ordinary skill inthe art are therefore also within the scope of the present invention.Numerous modifications may be made by those skilled in the art withoutdeparting from the scope of the invention. Also, this invention includeswithout limitation each combination and permutation of one or more ofthe abovementioned implementations, embodiments and features.

What is claimed is:
 1. A method comprising: (a) a first electricalnetwork creating a first electric field between electrodes in a firstpair of electrodes; and (b) a second electrical network creating asecond electric field between electrodes in a second pair of electrodes,such that (i) the first and second electric fields constructively anddestructively interfere with each other to create an amplitude-modulatedwaveform and (ii) the largest envelope amplitude of theamplitude-modulated waveform occurs in a brain; wherein, during steps(a) and (b) of this claim 1, the first and second electrode pairs areelectrically connected to the brain.
 2. The method of claim 1, whereinthe first electrode pair and second electrode pair are positionedside-by-side.
 3. The method of claim 1, wherein: (a) the amplitudemodulated waveform has an envelope amplitude; and (b) the firstelectrode pair and second electrode pair are positioned such that, at agiven time, the largest magnitude of the envelope amplitude occurs inonly one region of the brain, which region is path-connected andconsists only of those points at which the magnitude of the envelopeamplitude is equal to the largest magnitude.
 4. The method of claim 3,wherein the region spatially coincides with cortical tissue of thebrain.
 5. The method of claim 3, wherein the region spatially coincideswith subcortical tissue of the brain.
 6. The method of claim 1, wherein:(a) the amplitude modulated waveform has an envelope amplitude; (b) thegreatest magnitude of the envelope amplitude occurs in a spatialposition in the brain; (c) a volume exists, which volume consists ofonly those points at which the magnitude of the envelope amplitude isequal to at least 50% of the greatest magnitude; and (d) this volumecoincides with both cortical and subcortical tissue of the brain. 7.(canceled)
 8. (canceled)
 9. (canceled)
 10. The method of claim 3,wherein: (a) the first and second pairs of electrodes are implantedinside the brain; and (b) the minimum distance between the region andthe electrodes in the first and second pairs of electrodes is at least0.9 times the minimum distance between the first and second pairs ofelectrodes.
 11. (canceled)
 12. (canceled)
 13. (canceled)
 14. The methodof claim 1, wherein the amplitude-modulated waveform entrains neurons ina portion of the brain.
 15. The method of claim 1, wherein: (a) theamplitude-modulated waveform includes a sequence of peaks; and (b) theamplitude-modulated waveform stimulates neurons in at least a portion ofthe brain such that the neurons undergo a sequence of action potentialsthat is time-locked to the sequence of peaks.
 16. (canceled) 17.(canceled)
 18. The method of claim 1, wherein the first and secondelectric fields are temporally asymmetric.
 19. (canceled)
 20. The methodof claim 1, wherein the first and second electric fields are aperiodic.21. (canceled)
 22. An apparatus comprising: (a) a first electricalnetwork for creating a first electric field between electrodes in afirst pair of electrodes; and (b) a second electrical network forcreating a second electric field between electrodes in a second pair ofelectrodes, such that (i) when the first and second pairs of electrodesare electrically connected to a brain, the first and second electricfields constructively and destructively interfere with each other tocreate an amplitude-modulated waveform, and (ii) the largest envelopeamplitude of the amplitude-modulated waveform occurs in the brain. 23.(canceled)
 24. The apparatus of claim 22, wherein the first electrodepair and second electrode pair are configured to be positioned suchthat, at a given time, the largest magnitude of the envelope amplitudeoccurs in only one region of the brain, which region is path-connectedand consists only of those points at which the magnitude of the envelopeamplitude is equal to the largest magnitude. 25-27. (canceled)
 28. Theapparatus of claim 22, wherein: (a) the first electrical networkcomprises a first waveform generator, a first set of one or moredependent current sources, and a first pair of electrodes, (b) the firstwaveform generator is configured to control the first set of currentsources, (c) the first set of current sources is configured to createone or more electrical currents such that the first pair of electrodescreates the first electrical field, (d) the second electrical networkcomprises a second waveform generator, a second set of one or moredependent current sources, and a second pair of electrodes, (e) thesecond waveform generator is configured to control the second set ofcurrent sources, and (f) the second set of current sources is configuredto create one or more electrical currents such that the second pair ofelectrodes creates the second electrical field.
 29. (canceled)
 30. Theapparatus of claim 28, wherein: (a) the first set of current sourcescomprises a first current source and a second current source; (b) apositive input terminal of the first current source is electricallyconnected to the first waveform generator and a negative input terminalof the first current source is electrically connected to ground; and (c)a negative input terminal of the second current source is electricallyconnected to the first waveform generator and a positive input terminalof the second current source is electrically connected to ground. 31.The apparatus of claim 24, wherein the first and second pairs ofelectrodes are configured to be implanted inside the brain, such that,at a time when the first and second pairs of electrodes are implantedinside the brain, the minimum distance between the region and theelectrodes in the first and second pairs of electrodes is at least 0.9times the minimum distance between the first and second pairs ofelectrodes. 32-64. (canceled)
 65. A method comprising: (a) a firstelectrical network creating a first electric field between electrodes ina first pair of electrodes; and (b) a second electrical network creatinga second electric field between electrodes in a second pair ofelectrodes, such that (i) the first and second electric fieldsconstructively and destructively interfere with each other to create anamplitude-modulated waveform and (ii) the largest envelope amplitude ofthe amplitude-modulated waveform occurs in a heart; wherein, duringsteps (a) and (b) of this claim 1, the first and second electrode pairsare electrically connected to the heart.
 66. The method of claim 65,wherein the first electrode pair and second electrode pair arepositioned side-by-side.
 67. (canceled)
 68. The method of claim 65,wherein: (a) the first electrical network comprises a first waveformgenerator, a first set of one or more dependent current sources, and afirst pair of electrodes, (b) the first waveform generator controls thefirst set of current sources, (c) the first set of current sourcescreates an electrical current that flows through the first pair ofelectrodes; (d) the second electrical network comprises a secondwaveform generator, a second set of one or more dependent currentsources, and a second pair of electrodes, (e) the second waveformgenerator controls the second set of current sources, and (f) the secondset of current sources creates an electrical current that flows throughthe second pair of electrodes.
 69. (canceled)
 70. The method of claim68, wherein: (a) the first set of current sources comprises a firstcurrent source and a second current source; (b) a positive inputterminal of the first current source is electrically connected to thefirst waveform generator and a negative input terminal of the firstcurrent source is electrically connected to ground; and (c) a negativeinput terminal of the second current source is electrically connected tothe first waveform generator and a positive input terminal of the secondcurrent source is electrically connected to ground. 71-88. (canceled)